Approximation of Kolmogorov–Smirnov test statistic

Long Bai; David Kalaj

doi:10.1080/17442508.2020.1844705

Approximation of Kolmogorov–Smirnov test statistic

Long Bai^*
, David Kalaj

^*Corresponding author for this work

Department of Financial and Actuarial Mathematics

University of Montenegro

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

Motivated by the weak limit of Kolmogorov–Smirnov test statistics, in this contribution, we derive the asymptotics of (Formula presented.) for large u, where (Formula presented.) is the multivariate Brownian sheet based on a distribution function F. The asymptotic results are obtained for general F and some important examples are also shown.

Original language	English
Pages (from-to)	993-1027
Number of pages	35
Journal	Stochastics
Volume	93
Issue number	7
DOIs	https://doi.org/10.1080/17442508.2020.1844705
Publication status	Published - 2021

Keywords

Brownian sheet
Exact asymptotics
Gaussian fields
Kolmogorov–Smirnov test
Primary 60G15
Secondary 60G70

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10.1080/17442508.2020.1844705

Cite this

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title = "Approximation of Kolmogorov–Smirnov test statistic",

abstract = "Motivated by the weak limit of Kolmogorov–Smirnov test statistics, in this contribution, we derive the asymptotics of (Formula presented.) for large u, where (Formula presented.) is the multivariate Brownian sheet based on a distribution function F. The asymptotic results are obtained for general F and some important examples are also shown.",

keywords = "Brownian sheet, Exact asymptotics, Gaussian fields, Kolmogorov–Smirnov test, Primary 60G15, Secondary 60G70",

author = "Long Bai and David Kalaj",

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year = "2021",

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AU - Bai, Long

AU - Kalaj, David

PY - 2021

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N2 - Motivated by the weak limit of Kolmogorov–Smirnov test statistics, in this contribution, we derive the asymptotics of (Formula presented.) for large u, where (Formula presented.) is the multivariate Brownian sheet based on a distribution function F. The asymptotic results are obtained for general F and some important examples are also shown.

AB - Motivated by the weak limit of Kolmogorov–Smirnov test statistics, in this contribution, we derive the asymptotics of (Formula presented.) for large u, where (Formula presented.) is the multivariate Brownian sheet based on a distribution function F. The asymptotic results are obtained for general F and some important examples are also shown.

KW - Brownian sheet

KW - Exact asymptotics

KW - Gaussian fields

KW - Kolmogorov–Smirnov test

KW - Primary 60G15

KW - Secondary 60G70

UR - https://www.scopus.com/pages/publications/85096112911

U2 - 10.1080/17442508.2020.1844705

DO - 10.1080/17442508.2020.1844705

M3 - Article

AN - SCOPUS:85096112911

SN - 1744-2508

VL - 93

SP - 993

EP - 1027

JO - Stochastics

JF - Stochastics

IS - 7

ER -

Approximation of Kolmogorov–Smirnov test statistic

Abstract

Keywords

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